EVENT DETAILS AND ABSTRACT

Title: Bergman kernel and pluripotential theory
Speaker: Zbigniew Blocki
Speaker Info: Jagiellonian University and Indiana University
Brief Description:
Special Note: Note unusual time and location
Abstract:

We discuss some applications of pluripotential theory for the Bergman kernel and metric. In particular, the pluricomplex Green function can be used to prove Bergman completeness of a large class of domains (much bigger that had been known before). It is also applied to estimate the Bergman kernel from below, and recently very accurate estimates of this kind have been obtained. The main tools are the dbar-operator and the Monge-Ampère equation. Most of the results are new and nontrivial already in dimension one. For convex domains such a lower bound can be used to simplify Nazarov's complex analytic approach to the Bourgain-Milman inequality in convex analysis.